Adaptive L1-norm principal-component analysis with online outlier rejection

Panos Markopoulos, Mayur Dhanaraj, Andreas Savakis

Abstract: L1-norm principal-component analysis (L1-PCA) is known to attain sturdy resistance against faulty points (outliers) among the processed data. However, computing the L1-PCA of large datasets, with high number of measurements and/or dimensions, may be computationally impractical; in such cases, incremental solutions could be preferred. At the same time, in many applications it is desired to track the signal subspace via principal component adaptation. In this paper, we present new methods for both incremental and adaptive L1-PCA. Our first algorithm computes L1-PCA incrementally, processing one measurement at a time and performing online rejection of possible outliers; due to its low computational and storage cost, this algorithm is appropriate for application to both large and streaming datasets. Our second algorithm combines the merits of the first one with the additional ability to track changes in the nominal signal subspace. The proposed algorithms are evaluated with experimental studies on subspace estimation/tracking, video surveillance, image conditioning, and direction-of-arrival estimation/tracking.